Romeo comes from the Montague family and Juliet is a Capulet. The reason for the long-standing feud between the two families is not given, but it also causes the deaths of two other family members, Mercutio and Tybalt. The two families are reconciled in the end.

The two "houses", as Shakespeare calls them, are the Capulet and Montague households. Romeo is the son of Lord Montague, and Juliet the daughter of Lord Capulet. Tybalt is a cousin to Juliet - Lady Capulet's brother's child. Both families lose their heirs at the end of the play - the younger generation is wiped out.

Just to clarify, Paris and Mercutio are kinsmen of the royal family - relations of the prince, and do not belong to either family; though, by the end of the play, the two do end up dead.